Thesis Title: Modeling and Improvement of Processes with Heterogeneous Sources of Data

Advisors: Dr. Kamran Paynabar and Dr. Jianjun Shi

Committee members: 

Dr. Nagi Gebraeel

Dr. Yajun Mei

Dr. Bianca Maria Colosimo (Department of Mechanical Engineering, Politecnico di Milano)

Date and Time: Thursday, May 9, 2019, 11:00 am

Location: Groseclose 402

Abstract:

Integrating heterogenous data in an effective manner to construct an efficient model of a system is the main theme of this Thesis. Heterogeneity of data may refer to different levels of accuracy of data, different levels of information that process inputs (specifically functional inputs) may contain in explaining an output, or different forms of data. In this thesis, we will built upon the existing works and methods related to each of these classes of heterogeneity, and introduce methodologies to address existing challenges in practice.

In Chapter I we address the problem of collecting HA data adaptively and sequentially so when it is integrated with the LA data a more accurate surrogate model is achieved. For this purpose, we propose an approach that takes advantage of the information provided by LA data as well as the previously selected HA data points and computes an improvement criterion over a design space to choose the next HA data point.

In Chapter 2, we propose a functional regression method in which an functional response is estimated and predicted through a set of functional covariates. To deal with the functional variables, the functional regression coefficients are expanded through a set of low-dimensional smooth basis functions, making the estimation tractable while preserving the essential information of the covariates and response. In order to estimate the low-dimensional set of parameters and to deal with a large number of functional variables a penalized loss function with both smoothing and group lasso penalties is defined. The Block Coordinate Decent (BCD) method is employed to develop a scalable, iterative, and computationally tractable algorithm for minimizing the loss function and estimating the regression parameters.

In Chapter 3, we address the problem of estimating a process output, measured by a scalar, curve, image, or structured point cloud by a set of heterogeneous process variables such as scalar process setting, profile sensor readings, and images. We introduce a general multiple tensor-on-tensor regression (MTOT) approach in which each set of input data (predictor) and output measurements are represented by tensors. We formulate a linear regression model between the input and output tensors and estimate the parameters by minimizing a least square loss function. In order to avoid overfitting and reduce the number of parameters to be estimated, we decompose the model parameters using several basis matrices, and provide efficient optimization algorithms for learning the basis and coefficients.